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Exam4EquationSheet

# 1296 conductor thatmagnetic proportional to r the

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Unformatted text preview: aequals r loop,I B current has I time rate of S dt a S a (center 2 N of dBx S coil, inducing BI S eop 29.1–29.6.) conductor: thatmagnetic proportional to r. The magnetic B 0 NI B nitude is inversely z a current has a mag- dB 2ExamplesB = mExample 28.6.) 8.3 Ox S current in the coil. change of S (28.17) long, straight conductor carryingmagnetic Iﬂux through the loop. This relationx S multiB IB PSu N S I e law N m2aI d l : r ﬁeld lines are circles is validwith r. Thethe withBdirec-x is caused by a S 0 ship coaxial whether magnetic B nitude that is inversely proportional to the wire, ﬂux change I dP S S dB (28.6) right-hand rule. (See S S r (center of N circular loops)given by the Examples 28.3 CHAPTERtionsare circles changing magnetic ﬁeld, direc-dBxof the loop, or both. ted by B B 2ﬁeld lines 4p S coaxial with the wire, dB motion with r dB and 28.4.) S S e ﬁeld Ampere’s law: Ampere’sright-hand rule. (See line integral 0 ^ f tions given by the law states that the ExamplesdB 5 rS (See Examples 29.1–29.6.)28.3 A B d l = m0 Iencl (28.20) S m0 II ¿ S F rs: S r law: I I S S of B around induced current equals m0 times S B Axis of d the net curand 28.4.) z’sfrom Lenz’s law states that anany closed path or emf alwaysI tendsLto oppose lor cancel out = (28.11) Change in B B0 r du B S tract if 948 2pr through the area S ya S d r S f CHAPTER 28can be derivedMagnetic dB 5 TheBpositive Field S l S S ntegral that causedrentLenz’s lawMagnetic enclosed byFaraday’s law andconductors: change L B dSFaraday’s law: Sources of betweenthe path.the induced B easier to F d £ ¿ it. m I from current-carrying Fis often use. m0 II S I B l = 0 encl (28.20) force S S Faraday’s law states thatI F emf I B S A duB the = (28.11) SI d L dS l B (increasing) net cureB Examples 29.7 and 29.8.) current is determined current-carrying conductorsBattract ifE = - 2pr (29.3) sense of rthe timer rate of Two long, parallel, by a right-hand rule.S(See B L m II ¿ S SS S in a closed loop equals the negative of r conductors: orce B dt 2.) ISS BF Magnetic force between the same direction and ddu f if the F current-carrying B B 0 dB I ositive I S Examples 28.7–28.10.) are in the I I FL E The S B u n their changedue long,currents current-carrying conductors magnetic ﬁelds caused by several current(28.11) of to currentﬂux through the loop. ThisSrepel if L = 2pr distributions: The table dlists attract distributions. In each case the con- magnet’s S parallel, r dl e. (See Magnetic ﬁeldsTwo magneticare in oppositelaw: Lenz’s law relation- an induced current or emf always tends to oppose or cancelFout B otion causes a SS currents m S Lenz’s directions. The magnetic that I I NS B B states force S tion of S validper unit the same direction and repel if the whether ductor isship isthe current Iare in theﬂux change isBcausedSby a on their carrying currents . length between the conductors depends I F Binduced 948 CHAPTER 28 Sources of Magnetic Field B it. Lenz’s law can be derived from Faraday’...
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